Numerical modeling of radiation-induced charge
loss in CMOS floating gate cells
Modelización numérica de la pérdida de carga inducida por radiación en celdas CMOS
de puerta flotante
L. Sambuco Salomone
#1
, M. A. Garcia-Inza
#
, S. Carbonetto
#
, A. Faigón
#
#
Laboratorio de Física de Dispositivos - Microelectrónica, INTECIN, Facultad de Ingeniería, Universidad de Buenos
Aires - CONICET
Av. Paseo Colón 850, CABA, Argentina
1
lsambuco@fi.uba.ar
Abstract—The radiation response of programmed/erased
floating gate cells is studied by numerical simulations through
a recently developed physics-based numerical model. The role
played by oxide trapped charge in the overall threshold voltage
shift with dose is properly evaluated by varying the capture
rate of radiation-generated holes. A simplified analytical model
is considered, and its limitations are discussed.
Keywords: radiation effects; floating gate cells; numerical
modeling.
Resumen—Mediante un modelo numérico desarrollado
recientemente y basado en principios físicos, se estudia la
respuesta a la radiación de celdas de compuerta flotante
programadas/borradas. El rol que juega la captura de carga en
los óxidos en el desplazamiento total de la tensión umbral con
la dosis es debidamente evaluado a través de la variación de la
tasa de captura de los huecos generados por radiación. Se
considera un modelo analítico simplificado y se discuten sus
limitaciones.
Palabras clave: efectos de radiación; celdas de puerta flotante;
modelización numérica.
I. INTRODUCTION
Floating gate (FG) cells are conventional metal-oxide-
semiconductor field-effect transistors (MOSFETs) with the
addition of a polysilicon layer embedded in the gate oxide,
between the control gate and the silicon substrate. The
device is schematically shown in Fig. 1. As the floating gate
is electrically isolated, it serves as a charge storage layer,
making the whole structure a nonvolatile memory. The
charge at the floating gate can be manipulated by carrier
injection through the thin oxide layer between the floating
gate and the channel, known as the tunnel oxide. The
control gate usually aids this process and also is used to read
the state of the cell. Due to their high density, small power
consumption, and large program/erase cycling endurance,
floating gate cells are the standard devices for nonvolatile
memory applications. However, they are known to be
sensitive to ionizing radiation, either due to the peripheral
circuitry [2]-[3], or to the loss of the charge stored in the FG,
ultimately leading to bit errors, as observed in planar [4]-[5],
and in novel 3D technologies [6]. On the other hand, this
radiation sensitivity can be seized, so different floating gate-
based dosimeters were proposed [7]-[13]. One of the
advantages of a FG cell compared to a conventional MOS
dosimeter is that the charge preinjected into the floating gate
generates the necessary oxide electric field to increase the
effective radiation-induced electron-hole pair generation,
making it possible to achieve a good sensitivity even if the
sensor is unbiased during irradiation [8].
Either to mitigate radiation effects to employ FG cells in
space environments, or to exploit them for dosimetry
purposes, it is mandatory to have a physical model that
deals with radiation-induced floating gate charge loss in a
programmed/erase cell. Snyder et al. [14], proposed an
analytical model for the dose evolution of the threshold
voltage, based on the main mechanisms responsible for the
floating gate charge loss. This model was later extended to
modern technologies by other authors [15]-[16]. However,
the predictive capability of this model was disputed [17], so
that more accurate physics-based models are needed to
reproduce and predict the response of FG cells exposed to
ionizing radiation. For that purpose, we developed a
physics-based numerical model that self-consistently solves
the set of equations describing total dose effects in FG cells
[18].
The aim of this work is twofold: for one hand we explore
what a physics-based numerical model can unveil regarding
the role played by charges trapped in both oxides during the
exposure to radiation of a programmed/erased FG cell, and
on the other hand we compare it with the Snyder model.
Fig. 1. Schematic representation of a floating gate p-channel transistor.
II. THEORY
A. Physics-based numerical model
Figure 2 summarizes the main physical processes that
take place when a programmed cell is exposed to ionizing
radiation. Next, we briefly describe how the model works.
Revista elektron, Vol. 5, No. 2, pp. 100-104 (2021)
ISSN 2525-0159
100
Recibido: 07/10/21; Aceptado: 04/11/21
Creative Commons License - Attribution-NonCommercial-
NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
https://doi.org/10.37537/rev.elektron.5.2.136.2021
Original Article
For more details about modeling of total dose effects in
MOS oxides, the reader can refer to [19]-[21].
Fig. 2. Band diagram schematic representation of the physical model for a
floating gate structure with zero applied bias and negative charge initially
at the floating gate. charge generation and initial recombination,
electron (blue) and hole (red) transport, hole trapping, trapped hole
neutralization through electron trapping, and charge injection into the
floating gate.
Radiation generates electron-hole pairs within both
oxides, a fraction of which escapes from initial
recombination. Remaining carriers move drifted by the
electric field. Once a hole is within a small radius around an
oxygen vacancy, there is a probability for it to be trapped
there. Electron capture at a positive charged defect leads to
trapped hole neutralization. Charge in the floating gate
varies according to the injection of carriers from both oxides.
The system of equations to be solved is the following,
( )
t f f
ox
dF q
p p n
dx
= − + −
(1)
f
n
g n f t
dn
dj
R R n p
dt dx
= − + −
(2)
( )
fp
g c f t t
dp dj
R R p P p
dt dx
= − + − −
(3)
( )
t
c f t t n f t
dp
R p P p R n p
dt
= − −
(4)
,,
fg
p fg n fg
dp
jj
dt
=−
(5)
where n
f
and p
f
are the densities of free electrons and holes,
respectively, p
t
is the density of trapped holes, P
t
is the
density of traps, p
fg
is the carrier density at the floating gate,
R
c
and R
n
are the trapping and neutralization rates,
respectively. The generation rate is R
g
= g
0
YD
r
, where
g
0
= 8.1×10
14
cm
-3
Gy
-1
, Y is the fractional yield, and D
r
is
the dose rate. x is referred to the Si/SiO
2
interface. F is the
electric field, q is the elementary charge and ε
ox
is the SiO
2
permitivity (3.9ε
0
). The electron (j
n
) and hole (j
p
) fluxes are
described by the usual drift-diffusion model. j
n,fg
and j
p,fg
are
the electron and hole fluxes across both oxide/floating gate
interfaces, respectively.
The V
t
-shift due to charge in the oxides and the floating
gate is calculated using,
( )
0
to ip
tt
t t to ip fg ip
ox
q
V p t t x dx p t
+
= − + − +
(6)
where t
to
and t
ip
are the tunnel and interpoly oxides
thicknesses, respectively. Free carriers were neglected due
to their much lower concentrations relative to the trapped
charge.
B. Snyder model
In 1989, Snyder et al. [14] presented a simplified model
for the discharge of floating gate cells during irradiation.
This model is based on the same physics previously
described with the addition of photoemission of carriers
from the floating gate into the oxides. However, the
distinctive feature of the Snyder model depends on the
following two assumptions: (i) holes are trapped within the
oxides close to the corresponding FG/SiO
2
interface, and (ii)
fractional yield depends linearly on electric field, which
allow to reduce the V
t
evolution with dose to the following
first order expression,
( )
00
exp
tt
V V D D = −
(7)
where D is the absorbed dose, and ΔV
t0
and D
0
are the
fitting parameters representing the total V
t
-shift and a
characteristic dose, respectively.
III. RESULTS AND DISCUSSION
The floating gate devices considered in simulations are
p-channel MOSFETs from a 1.5 μm complementary MOS
(CMOS) process. The thickness of the tunnel and interpoly
oxides are t
to
= 30 nm and t
ip
= 57 nm, respectively. Also,
we assume γ-irradiation. For other irradiation source, the
expression for the electric field dependence of the fractional
yield must be modified.
Simulations of the radiation response of FG cells with
different initial V
t
values, corresponding to different initial
charge at the floating gate, were performed. As a first case,
we considered a capture rate R
c
= 10
-14
cm
3
s
-1
, low enough
for the oxide trapped holes contribution to be non-relevant,
so the dynamic is dominated by the injection of carriers into
the floating gate. Neutralization rate was R
n
= 10
-6
cm
3
s
-1
,
although the response is almost independent of it, given the
low value of R
c
. The results are shown in Fig. 3. The V
t
vs.
dose curves are consistent with the progressive loss of the
charge stored at the floating gate with the device reaching a
final V
t
value independent of the initial condition and
corresponding to the cell with minimal amount of stored
charge. Also, each curve was fitted with Snyder model
expression (7). As the initial charge at the floating gate
increases, the first order fit is worse, tending to overestimate
the discharge for low dose, whereas the opposite occurs for
high dose. Particularly relevant is the analysis of the
characteristic dose D
0
needed to reproduce the results. First,
it is observed that D
0
is independent of whether the initial
charge in the floating gate is positive or negative, which is
expected because of the low R
c
value that leads to responses
dominated by the injection in the floating gate of carriers
generated in both oxides. Second, D
0
increases with the
magnitude of this initial charge. This result is consistent
with previously reported results [17], and differs with the
assumption made by Snyder model about D
0
depending
only on external bias. Physically, this result can be
explained because of the sublinear dependence of the
fractional yield on electric field. In other terms, the amount
Revista elektron, Vol. 5, No. 2, pp. 100-104 (2021)
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of charge needed to restore the device to the chargeless
condition is equal to the initial charge at the floating gate
p
fg0
. As p
fg0
increases, the electric field in both oxides
increases and a higher fraction of electron-hole pairs escape
from the initial recombination, but as this yield is not
strictly linear with electric field, more dose is needed to
generate the amount of charge that compensates for the
excess of electrons in the floating gate.
Fig. 3. Numerical simulations (symbols) and Snyder’s first order fits (lines)
of the floating gate charge loss for different initial conditions and R
c
= 10
-14
cm
3
s
-1
, and R
n
= 10
-6
cm
3
s
-1
. Characteristic dose values D
0
are 326 Gy for
p
fg0
= ±1×10
12
cm
-2
, 433 Gy for p
fg0
= ±2×10
12
cm
-2
, and 539 Gy for
p
fg0
= ±3×10
12
cm
-2
.
To evaluate the impact that hole trapping within the
oxides has on the response, simulations were made with an
initial charge p
fg0
= ±2×10
12
cm
-2
, neutralization rate
R
n
= 10
-6
cm
3
s
-1
, and two values for the capture rate R
c
. The
results are shown in Fig. 4. As observed, when
R
c
= 10
-12
cm
3
s
-1
the steady state V
t
value differs from the
one corresponding to a completely discharged cell, but it is
shifted towards negative voltages due to the holes trapped in
both oxides. Again, the Snyder expression (7) was used to
fit the curves, failing to reproduce the long-term behaviour
of the curves with the higher R
c
value, especially when the
floating gate is initially filled with electrons. Also, when
hole capture becomes relevant, the characteristic dose D
0
starts to depend on whether the cell is initially programmed
or erased.
Fig. 4. Numerical simulations (symbols) and Snyder first order fits (lines)
of the floating gate charge loss for p
fg0
= ±2×10
-12
cm
-2
, R
n
= 10
-6
cm
3
s
-1
,
and different R
c
values.
To get some insight about the microscopic processes
involved in the radiation response, Fig. 5 shows the ΔV
t
contributions due to the charge at the floating gate (ΔV
t(fg)
),
and holes trapped in tunnel (ΔV
t(to)
) and interpoly (ΔV
t(ip)
)
oxides for the two simulations of Fig. 4 that start with a
programmed cell (p
fg0
= -2×10
12
cm
-2
). For a low capture
rate, the response is dominated by the variation of the
charge at the floating gate, whereas for the higher capture
rate value, it is observed that the hole trapping within the
oxides does not allow the floating gate to be totally
discharged. Not only a remnant of the electrons initially at
the floating gate remain there at the end of the irradiation,
but also the trend in the change can even turn around and
the density of electrons at the floating gate increases slightly
for high doses. As the final V
t
value is lower than that for a
device without charge, the contribution of holes trapped in
both oxides overcompensate the electrons in the floating
gate. It is worth to notice that the ΔV
t
contribution due to
holes trapped within the interpoly oxide is not monotone.
Fig. 5. Contributions to the overall ΔV
t
due to charges at the floating gate
and trapped in both oxides from the simulations of Fig. 4 that start with
p
fg0
= -2×10
-12
cm
-2
. Solid lines correspond to R
c
= 10
-12
cm
3
s
-1
, and dashed
lines correspond to R
c
= 10
-14
cm
3
s
-1
. In both cases, R
n
= 10
-6
cm
3
s
-1
.
Figure 6 shows the conduction band electronic energy
across the structure for different accumulated dose during
the irradiation of a floating gate cell with an initial charge
p
fg0
= -2×10
12
cm
-2
, and physical parameters
R
c
= 10
-12
cm
3
s
-1
and R
n
= 10
-6
cm
3
s
-1
. The spatial
distributions of trapped holes in both oxides are shown in
Fig. 7. Due to the electric fields in each oxide, holes tend to
be accumulated towards the corresponding interfaces with
the floating gate. As accumulated dose increases and V
t
approaches saturation, the electric field vanishes in each
oxide leading to a charge redistribution process that narrows
the spatial distribution of trapped holes towards the
interfaces.
Revista elektron, Vol. 5, No. 2, pp. 100-104 (2021)
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Fig. 6. Conduction band electronic energy as a function of distance for the
simulation of floating gate charge loss with p
fg0
= -2×10
-12
cm
-2
,
R
c
= 10
-12
cm
3
s
-1
and R
n
= 10
-6
cm
3
s
-1
from Fig. 4.
Fig. 7. Spatial distribution of trapped holes within (a) tunnel, and (b)
interpoly oxides, for different accumulated doses for the simulation of
floating gate charge loss with p
fg0
= -2×10
-12
cm
-2
, R
c
= 10
-12
cm
3
s
-1
and
R
n
= 10
-6
cm
3
s
-1
from Fig. 4.
IV. CONCLUSIONS
The charge loss of programmed/erased floating gate cells
due to ionizing radiation exposure at zero bias was studied
by means of numerical simulations with a recently
developed physics-based model. Once the initial charge at
the floating gate and capture and neutralization rates for
oxide traps are determined, the model predicts the dose
evolution of threshold voltage. Changing the capture rate
within the usual range reported in the literature showed that
the presence of oxide charges may become relevant, shifting
the long-term threshold voltage from its value for a non-
charged structure.
Numerical simulations were compared with the Snyder
model, which is based on a first order expression for the
relation between threshold voltage and absorbed dose. Both
models agree on the overall response. Nevertheless, for
large initial charge at the floating gate and/or for a
moderately high capture rate, the numerically simulated
responses departed from this simplified dose dependence.
Further comparison with experimental data will help to
conclude about the usefulness of both models.
In the future, we intend to extend the model to include
other floating gate structures, such as: (i) an oxide-nitride-
oxide (ONO) interpoly oxide [15]-[17], (ii) a trap-rich
dielectric as trapping layer, as in silicon-oxide-nitride-
oxide-silicon (SONOS) charge trapping memories [22]-[23],
and (iii) a floating gate that extends over a field oxide for
increasing sensitivity in dosimetry applications [7].
ACKNOWLEDGMENT
This work was supported by grants UBACYT
20020190200002BA and 20020170100685BA.
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